For the free-falling bungee jumper with linear drag (Prob. 1.5), assume a first jumper is 70 kg and has a drag coefficient of 12 kg/s. If a second jumper has a drag coefficient of 15 kg/s and a mass of 80 kg, how long will it take her to reach the same velocity jumper 1 reached in 9 s?

Data From Problem 1.5

Rather than the nonlinear relationship of Eq. (1.7), you might choose to model the upward force on the bungee jumper as a linear relationship:

Equation (1.7)

FU = −c′ν
where c′ = a first-order drag coefficient (kg/s).
(a) Using calculus, obtain the closed-form solution for the case where the jumper is initially at rest (v = 0 at t = 0).
(b) Repeat the numerical calculation in Example 1.2 with the same initial condition and parameter values. Use a value of 11.5 kg/s for c′.

Example 1.2

FU -Cav